The thing about using a router, though, is that you gain much more capabilities - more memory, more speed, etc; with the right router (actually, the wireless hard drive docking stations with USB port are the best, from what I can tell - but even the old-school bog-standard WRT54G isn't bad) you can easily have the processing power and memory equivalent of a 486; drop an SD adapter on it, and you're really set.
Granted, it isn't for everyone, and it is easy to brick the router - if all you need is data transfer over wifi or ethernet, probably not worth it (though wifi shields, etc still aren't as cheap as an old router) - but if you wanted to make an interactive (but simple) browser gui front end with an integrated IP camera, etc to control the Arduino - it can be an attractive option, if you're willing to take the time to do it.